Question

The product of two roots of the given equation is -10.

10x^3 + 100x^2 = cx + 1000

Find the third root.

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Answer 1

Given : The product of two roots of the given equation is -10.

10x³ + 100x² = cx + 1000

To Find : the third root.

Solution:

10x³ + 100x² = cx + 1000

=> 10x³ + 100x² - cx - 1000 = 0

ax³ + bx² + cx + d  =   0

α  β  and γ are roots

α + β  + γ  = - b/a

α β  +  βγ  + α γ  = c/a

αβγ  = -d/a

10x³ + 100x² - cx - 1000 = 0

αβγ  = -d/a

=> αβγ  = - (-1000)/10

=> αβγ  = 100

product of two roots of the given equation is -10

third root is = 100/(-10)

= - 10

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